The wavelength of an X-ray beam is 10Aᵒ. The mass of a fictitious particle having the same energy as that of the X-ray photons is x/3h kg. The value of x is __________. (h = Planck's constant)

Solution

Physics sir · 3 steps

Set the photon's energy hc/λ equal to mc², and the mass comes out as h/(λ c).

1. Equate the energies. A photon of wavelength λ carries energy E = hc/λ. A particle of mass m has energy E = mc². The particle has the same energy as the photon, so set the two equal.

   mc² = hc/λ ⇒ m = h/(λ c)

2. Put in numbers. λ = 10 Å = 10 × 10⁻¹⁰ m = 10⁻⁹ m and c = 3 × 10⁸ m s⁻¹. So λ c = 3 × 10⁻¹ = 3/10, which gives m = 10/3h kg.
3. So. Comparing 10/3h with x/3h gives x = 10.

The common slip: 100. Taking 10 Å as 10⁻¹⁰ m instead of 10⁻⁹ m makes m = 100/3h, so x comes out as 100.

The idea to keep. Whenever a photon's energy is matched to a particle, equate hc/λ with mc². The result m = h/(λ c) is the photon's equivalent mass, the same as p/c.

Answer from the NTA final answer key. Solution by PrepWiser.